Particle-physics constraints on multifractal spacetimes

TL;DR

This paper derives experimental bounds on the scales of multifractal spacetime features by analyzing electroweak phenomena like muon decay and the Lamb shift, setting new limits on the characteristic scales of such theories.

Contribution

It provides the first robust experimental constraints on the scales where multifractal spacetime properties could influence physical processes.

Findings

Upper bounds on time scale: $t_* < 10^{-13}$ s and $t_* < 10^{-27}$ s

Energy scale constraint: $E_* > 35$ MeV and $E_* > 450$ GeV

Constraints on length scale: $ ext{less than } 10^{-19}$ m

Abstract

We study electroweak interactions in the multiscale theory with $q$-derivatives, a framework where spacetime has the typical features of a multifractal. In the simplest case with only one characteristic time, length and energy scale $t_*$, $\ell_*$, and $E_*$, we consider (i) the muon decay rate and (ii) the Lamb shift in the hydrogen atom, and constrain the corrections to the ordinary results. We obtain the independent absolute upper bounds (i) $t_* < 10^{-13}{\rm s}$ and (ii) $E_*>35\,\text{MeV}$. Under some mild theoretical assumptions, the Lamb shift alone yields the even tighter ranges $t_*<10^{-27}\,{\rm s}$, $\ell_*<10^{-19}\,{\rm m}$, and $E_*>450\,\text{GeV}$. To date, these are the first robust constraints on the scales at which the multifractal features of the geometry can become important in a physical process.